Universality, frustration, and conformal invariance in two-dimensional random Ising magnets

Abstract

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferromagnetic and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents ␥/, ␣/, and to be obtained, whenever a secondorder transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure-Ising exponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point along either the temperature axis or the Nishimori line, one finds nondiverging specific heats. A percolationlike ratio ␥/ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems. ͓S0163-1829͑99͒07533-5͔

Spin-correlation function of the fully frustrated Ising model and ±JIsing spin glass on a square lattice

“…The canonical model with p = 0.5 on a square lattice has been studied the most, and it is well received that spin glass behavior occurs at zero temperature [1][2][3][4][5][6] and persists down to a critical probability p c of about 0.11. [7][8][9][10][11][12][13][14][15][16][17][18] Good agreement for the values of ground state energy and entropy has been obtained by many researchers. However, up to the present there has been very little development in extending the method to a direct calculation of the spin correlation at zero temperature, and most of the results have been obtained by extrapolating the zero-temperature results.…”